The Stacks project

Definition 20.26.15. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{F}$, $\mathcal{G}$ be $\mathcal{O}_ X$-modules. The Tor's of $\mathcal{F}$ and $\mathcal{G}$ are define by the formula

\[ \text{Tor}_ p^{\mathcal{O}_ X}(\mathcal{F}, \mathcal{G}) = H^{-p}(\mathcal{F} \otimes _{\mathcal{O}_ X}^\mathbf {L} \mathcal{G}) \]

with derived tensor product as defined above.

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